As I consider myself to be an analyst first and foremost, I am interested in a wide range of analytical problems. However, within analysis I am most interested in Harmonic Analysis, Partial Differential Equations and Geometric Measure theory and the connection between these areas.
More specifically, I am working on solving boundary value problems for linear elliptic and parabolic PDEs using Harmonic Analysis techniques and results from Geometric Measure Theory.
Ulmer, M. Perturbation theory for the parabolic regularity problem, https://arxiv.org/abs/2408.12529
Ulmer, M. Lᵖ boundary value problems for elliptic and parabolic operators, Ph.D. thesis, University of Edinburgh, United Kingdom, July 2024, http://dx.doi.org/10.7488/era/4636
Ulmer, M. Solvability of the Dirichlet problem for a new class of elliptic operators, https://arxiv.org/abs/2311.00614
Dindoš, M., Sätterqvist, E. & Ulmer, M. Perturbation Theory for Second Order Elliptic Operators with BMO Antisymmetric Part. Vietnam J. Math. 52, 519–566 (2024). https://doi.org/10.1007/s10013-023-00653-z